A079276 Multiplicative inverse in the finite field F(prime(n)) of the product of the first n-1 primes modulo prime(n).

1, 2, 1, 4, 1, 3, 15, 18, 20, 12, 18, 27, 7, 5, 43, 2, 4, 10, 38, 3, 60, 20, 53, 62, 52, 83, 11, 30, 27, 49, 113, 63, 79, 25, 81, 143, 80, 121, 53, 142, 81, 52, 81, 150, 136, 40, 176, 114, 167, 138, 84, 46, 239, 213, 137, 4, 122, 136, 255, 141, 273, 30, 22, 25, 179, 9, 43, 12

Offset: 1

Author

Valentin F. Schmid (v_schmid(AT)hotmail.com), Feb 07 2003

Keywords

• nonn

Comments

a(n)=1 if and only if n-1 is in A341805. - Jeppe Stig Nielsen, Feb 20 2021

Examples

			a(6)=3 because 2*3*5*7*11 = 2310, 2310 == 9 (mod 13) and 9*(9^(-1)) == 9*3 == 1 (mod 13).
		

Links

• Eric Weisstein's World of Mathematics, Primorial

Crossrefs

Cf. A062347, A002110, A000040, A240673, A341805.

Programs

Maple

a := n -> (1/mul(ithprime(j), j=1..n-1)) mod ithprime(n);
seq(a(n), n=1..68); # Peter Luschny, Apr 13 2014

Mathematica

a[n_] := Module[{i}, Return[PowerMod[Product[Prime[i], {i, 1, n - 1}], -1, Prime[n]]]; ];

Formula

a(1) = 1; for n>1, a(n) = ( prime(n-1)# (mod prime(n)) )^(-1), where prime(i) is the i-th prime number, prime(i)# is the product of first i primes, x^(-1) is the multiplicative inverse in the finite field F(prime(n)).